This paper discusses the task of human action detection. It requires not only classifying what type the action of interest is, but also finding actions' spatial-temporal locations in a video. The novelty of this paper lies on two significant aspects. One is to introduce a new graph based representation for the search space in a video. The other is to propose a novel sub-volume search method by Minimum Cycle detection. The proposed method has a low computation complexity while maintaining a high action detection accuracy. It is evaluated on two challenging datasets which are captured in cluttered backgrounds. The proposed approach outperforms other state-of-the-art methods in most situations in terms of both Precision-Recall values and running speeds.